NEW YORK (AP) -- Henrik Lundqvist went from shaking his head in disgust to raising his arms in celebration when time finally ran out on the Washington Capitals.

Such is life as a New York Ranger these days.

Lundqvist was perfect in yet another nail-biting game that was razor close throughout the tension-filled, seven-game series, until the Capitals cut the Rangers' brief two-goal lead to one in the third period of Game 7. But Washington couldn't muster much else, and New York held on for a 2-1 victory on Saturday night that sent the top-seeded Rangers into the Eastern Conference finals against the No. 6 New Jersey Devils.

"We didn't expect the first blowout," said Rangers forward Brad Richards, who staked his team to a 1-0 lead just 1:32 in. "We expected another tight game. It came down to that again. It's just the way this series has gone, and it didn't change."

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Michael Del Zotto also scored for the Rangers, who enjoyed the two-goal lead for all of 38 seconds before Capitals defenseman Roman Hamrlik made it 2-1 with 9:17 remaining.

Coming into Game 7, these teams were tied or within one goal of each other for 90 percent of the time, and the finale provided much of the same.

Lundqvist finished with 22 saves for the Rangers, who improved to 5-0 in Game 7s at Madison Square Garden. Now they will face the Atlantic Division-rival Devils in a rematch of the 1994 East finals, won dramatically by New York on Stephane Matteau's double-overtime goal in Game 7. That propelled the Rangers toward their first Cup title in 54 years.

It was that series that truly put this regional rivalry on an international stage. With stars on both sides, the Rangers and Devils, separated by just six miles and the Hudson River, played 27 periods of dramatic, tense hockey that ultimately resulted in each team winning a Stanley Cup over the next 13 months.

The Rangers have beaten the Devils in four of their five previous playoff meetings.

This next installment will open Monday in New York. The Devils have been off since eliminating the Philadelphia Flyers in Game 5 on Tuesday.

"It feels good to get that win," Rangers forward Marian Gaborik said. "You have to enjoy it for a little bit, but Monday we start from scratch again. We need to feel good about ourselves and get ready for the next series."

New York and Washington alternated wins and losses from Game 1 on, and this one didn't come easy for the Rangers, who missed a chance to eliminate the Capitals in Game 6 on the road.

It was yet another heartbreaker for Washington, which was trying to reach the conference finals for the third time. Six of the Capitals' seven playoff losses were by one goal, and only one of their 14 games overall were decided by more than one.

As they came off the ice following the final buzzer, the Capitals could be seen and heard smashing their sticks against the wall as they headed down the hallway to their dressing room.

"It's disappointing," said Braden Holtby, who made 29 saves. "We really did believe in here that we had the team to do it all. We gave ourselves a great chance. It's a tough loss. What we can take out of it is that New York is a very good team. We didn't leave anything on the table."

Before the cheering subsided following Del Zotto's goal, Hamrlik sent a shot off New York forward Derek Stepan that fluttered past Lundqvist for his only blemish of the night and left him shaking his head.

Suddenly, the jubilant crowd was thrown back into a state of nervousness, even though the score board pleaded all night for the fans to "Believe."

"Anytime you experience a surge like this, the momentum can turn. But we didn't let it happen," Del Zotto said. "We weren't happy about some of our play in the middle period but we found a way to keep them at bay."

The shots were 12-11 in favor of the Rangers in the scoreless second period, and New York took over in the third with an 11-4 edge.

Both the Rangers and the Capitals reached the second round of this year's playoffs with Game 7 wins. New York knocked out Ottawa, and seventh-seeded Washington eliminated the defending Stanley Cup champion Boston Bruins.

History isn't all on the Rangers' side. Since playoff expansion, no club has played 14 games in the first two rounds and went on to capture the Cup. They did reverse a recent trend in which Washington eliminated them from the playoffs in two of the previous three years, including the Capitals' comeback from a 3-1 series deficit in the first round in 2009.

New York played a very disciplined game, taking only one penalty for delay of game against Ruslan Fedotenko in the third period. The Rangers' power play did nothing on its two chances, but keeping Washington's man-advantage unit off the ice helped secure this win.

The Capitals tried to pull Holtby for an extra skater with 1:22 left in the game, but he had to scramble back to cover the vacated net before he ever got to the bench.

He finally got off the ice, and the Capitals pressured in the Rangers' end. The puck was stuck in the corner when the final seconds ran out, and Lundqvist thrust both arms in the air as streamers poured down from the ceiling.

Matching the Capitals' quick start in Game 6, the Rangers jumped out quickly and took a 1-0 lead when Richards scored on New York's first shot.

Carl Hagelin used his speed to chase down a dump-in in the lower right corner of the Capitals' zone and curled behind the net with the puck on his backhand. As he came out the other side, Hagelin feathered a pass up to Richards, who one-timed a shot that beat Holtby inside the right post while Gaborik was in front of the net.

It was Richards' team-leading fourth goal of the series and sixth of the playoffs.

"It's a big goal. It gets the nerves out," Richards said. "You don't exhale, but you have the 1-0 lead. You got the crowd in it. They're not waiting for something to happen.

"They did it to us in Game 6 when they got an early goal. We did that tonight."

Although Washington controlled the puck for large chunks of the game, the Capitals yet again couldn't overcome the dreaded 1-0 deficit. The team that scored first won all seven games in the series. The numbers were even more stark for the Capitals, who went 0-6 in the playoffs after allowing the first goal and 7-1 when they grabbed the first lead.

Del Zotto started and finished the Rangers' second scoring play. He leveled Capitals captain Alex Ovechkin in the New York and moved the puck up ice. He eventually took a pass from Gaborik and snapped a shot past Holtby.

However, before the cheers subsided, the Capitals got back within a goal on Hamrlik's first of the playoffs.

This one was tight throughout.

Washington was outshot 12-11 in the second period, that featured a blank score sheet with no goals and no penalties. Midway through the frame, the Capitals kept the pressure on the Rangers with Ovechkin's line on the ice and camped out in the New York end for about two minutes.

As the tired Rangers chased Washington all around their zone and unable to change any players, the Capitals moved the puck side to side and up and down, seemingly keeping Lundqvist on a swivel. Many of their shots were offline, but the Capitals produced several prime chances that Lundqvist turned away -- each one drawing sighs, but appreciative cheers from the towel-waving crowd.

"We came up short. We played a good team and a great goalie," Capitals forward Nicklas Backstrom said. "The Rangers played the way we played last game. They got a lead at the beginning and they controlled the game. We had some good puck possession in the second period but we couldn't get any real opportunities."

Mike Knuble had a good whack at the puck at the left post, but Lundqvist was there with his pad to keep it out.

Holtby, who became a father on Thursday, shook off Richards' early strike and seemed to gain confidence as the game wore on and the pressure built at the other end of the ice.

Notes: Richards, who improved to 4-0 in Game 7s, has recorded a goal and three assists in those games. He has seven goals and eight assists in the last 11 games in which his team has faced elimination. ... Hagelin, who had two assists, had his first points in 10 games, dating to an assist in New York's playoff opener against Ottawa. ... Injured Capitals forward Jay Beagle missed his second straight game, and Jeff Halpern took his place again. ... Fedotenko improved to 6-0 in Game 7.